The main aim of the work is to assess physical parameters of forest woodchips and their impact on the prices achieved by the supplier in transactions with a power plant. During fragmentation of logging residue, high content of green matter and contaminants negatively impacts the quality parameters that serve as basis for settlements. The analysis concerns data on the main parameters -water content, fuel value, sulphur and ash content -from 252 days of deliveries of forest chips to a power plant. The deliveries were realised from forested areas on an average about 340 km from the plant. Average water content and the resultant fuel value of forest chips was within 27-47% and 8.7-12.9 GJ×Mg −1 (appropriately), respectively. They depend on the month in which they are delivered to the power plant. The threshold values for the above-mentioned parameters are set by the plant at a real level and the suppliers have no problems with meeting them. The parameter that is most frequently exceeded is ash content (11.5% of cases). The settlement system does not differentiate on the basis of the transport distance but gives possibility to lower the settlement price when the quality parameters are not met but provides no reward for deliveries with parameters better than the average ones. On the basis of results obtained, it was calculated that average annual settlement price is lower than the contract price by about 0.20 PLN×GJ −1 , which in case of the analysed company may translate into an average daily loss of about 700 PLN.

PurposeThe paper aims to explore unavailability of dormant systems that are under both preventive and corrective maintenance. Preventive maintenance is considered as a failure based maintenance model, where full renew is realized at the occurrence of every nth failure. It proposes the imperfect corrective maintenance model, where each restoration process deteriorates the system lifetime, probability distribution of which is gradually changed via increasing failure rate.Design/methodology/approachBasic reliability mathematics necessary for unavailability quantification of a system which undergoes a real aging process with maintenance has been derived proceeding from renewal theory. New renewal cycle was defined to cover the real aging process and the expectation of its length was determined. All events resulting in the failure of studied system were explored to determine their probabilities. An integral equation where the unavailability function characterizing studied system is its solution was derived.FindingsPreventive maintenance is closely connected with the occurrence of the nth failure, which starts its renew. The number n can be considered as a parameter which significantly influences the unavailability course. The paper shows that the real aging process characterized by imperfect repairs can significantly increase the unavailability courses in contrast with theoretical aging. This is true for both monitored and dormant systems.Originality/valueAlthough mathematical methods used in this article were inspired and influenced by the work of reference (van der Weide and Pandey, 2015), derivation of final formulas for unavailability quantification considering the new renewal cycle is original. Idea of the real aging process is new as well. This paper fulfils an identified need to manage the maintenance of realistically aging systems.

ABSTRACT. The authors define a notion of system of sets with multiplicative asymptotic density in this paper. A criterion and one necessary condition for a given system A ito be a system with multiplicative asymptotic density is given. Properties of certain special types of systems of sets with multiplicative asymptotic density are treated.

In general, a complex system is composed of different components that are usually subject to a maintenance policy. We take into account systems containing components that are under both preventive and corrective maintenance. Preventive maintenance is considered as a failure-based preventive maintenance model, where full renewal is realized after the occurrence of every nth failure. It offers an imperfect corrective maintenance model, where each repair deteriorates the component or system lifetime, the probability distribution of which gradually changes via increasing failure rates. The reliability mathematics for unavailability quantification is demonstrated in the paper. The renewal process model, involving failure-based preventive maintenance, arises from the new corresponding renewal cycle, which is designated a real ageing process. Imperfect corrective maintenance results in an unwanted rise in the unavailability function, which can be rectified by a properly selected failure-based preventive maintenance policy; i.e., replacement of a properly selected component respecting both cost and unavailability after the occurrence of the nth failure. The number n is considered a decision variable, whereas cost is an objective function in the optimization process. The paper describes a new method for finding an optimal failure-based preventive maintenance policy for a system respecting a given reliability constraint. The decision variable n is optimally selected for each component from a set of possible realistic maintenance modes. We focus on the discrete maintenance model, where each component is realized in one or several maintenance mode(s). The fixed value of the decision variable determines a single maintenance mode, as well as the cost of the mode. The optimization process for a system is demanding in terms of computing time because, if the system contains k components, all having three maintenance modes, we need to evaluate 3k maintenance configurations. The discrete maintenance optimization is shown with two systems adopted from the literature.

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